Respuesta :
The expression is used to find m ∠ABC are [tex]\rm sin\theta = \dfrac{7.5}{9.8}[/tex] and [tex]\rm cos\theta = \dfrac{6.3}{9.8}[/tex].
Given that
Triangle ABC is shown. Angle BCA is a right angle.
The length of hypotenuse BA is 9.8 inches, the length of CB is 6.3 inches, and the length of CA is 7.5 inches.
We have to determine
Which expressions can be used to find m ∠ABC?
According to the question
To measure the angles for the triangles following all the steps given below.
In triangle ABC with right angle c.
Sine is the ratio of the length of the side that is opposite that angle, to the length of the longest side of the triangle (the hypotenuse),
The measure of the sin angle is equal to the opposite side by the hypotenuse.
[tex]\rm sin\theta = \dfrac{Opposite \ side }{Hypotenuse}\\ \\ [/tex]
The cosine is the ratio of the length of the side adjacent to the angle to the length of the hypotenuse.
The measure of the cos angle is equal to the adjacent side by the hypotenuse.
[tex]\rm cos\theta = \dfrac{Adjacent \ side }{Hypotenuse}\\ \\ [/tex]
On comparing with the measure of the angles.
[tex]\rm \theta = cos{-1}\dfrac{6.3}{9.8}\\ \\ cos\theta = \dfrac{6.3}{9.8}[/tex]
And on comparing with the sin angle.
[tex]\rm \theta = sin{-1}\dfrac{7.5}{9.8}\\\\sin\theta = \dfrac{7.5}{9.8}[/tex]
Hence, the expression is used to find m ∠ABC are [tex]\rm sin\theta = \dfrac{7.5}{9.8}[/tex] and [tex]\rm cos\theta = \dfrac{6.3}{9.8}[/tex].
To know more about Trigonometric Ratios click the link given below.
https://brainly.com/question/20382975
